Can You Solve It?

Please help me if you can. please show how you got the answer.

fomenos

Answer:

Step-by-step explanation:

The area of a circle is A = πr², where r is the radius. That means in order to solve this we have to find the value of x, which is the diameter of the lake, and then divide it in half to get the radius. To find x we will use similar triangles and proportions. x is the height of the big triangle and 4.5 is the height of the smaller triangle; 15.3 + 7.4 is the hypotenuse of the big triangle and 7.4 is the hypotenuse of the smaller triangle. Setting up our proportion:

$\frac{x}{4.5}=\frac{15.3+7.4}{7.4}$ which simplifies a bit to

$\frac{x}{4.5}=\frac{22.7}{7.4}$ and cross multiply to solve for x:

7.4x = 102.15 so

x = 13.8 That is the diameter of the lake. Divide it in half to get 6.9, the radius. Applying the area formula for a circle:

A = (3.14)(6.9)² and

A = 3.14(47.61) so

A = 149.5 which rounds to 150, Choice C

5 0

3 years ago

The diagonals of a parallelogram are perpendicular to each other. The perimeter of the parallelogram is 48 feet. Find the length

iVinArrow [24]

We know that a parallelogram has two pairs of congruent sides. If we know that the diagonals are perpendicular and the perimeter is 48 feet, we can solve is using the area of parraleogram formula: with that we get the answer of 5, and 9

3 0

4 years ago

Which equation represents the vertical line passing through (7,-3)?

Nimfa-mama [501]

Answer:

x = 7

Step-by-step explanation:

The equation of a vertical line has equation of the form

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (7, - 3) with x- coordinate 7 , thus

x = 7 ← equation of vertical line

3 0

3 years ago

Show that if X is a geometric random variable with parameter p, then

Lubov Fominskaja [6]

Answer:

$\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}=-\frac{p ln p}{1-p}$

Step-by-step explanation:

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

$P(X=x)=(1-p)^{x-1} p$

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

$X\sim Geo (1-p)$

In order to find the expected value E(1/X) we need to find this sum:

$E(X)=\sum_{k=1}^{\infty} \frac{p(1-p)^{k-1}}{k}$

Lets consider the following series:

$\sum_{k=1}^{\infty} b^{k-1}$

And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:

$\int_{0}^b \sum_{k=1}^{\infty} r^{k-1}=\sum_{k=1}^{\infty} \int_{0}^b r^{k-1} dt=\sum_{k=1}^{\infty} \frac{b^k}{k}$ (a)

On the last step we assume that $0\leq r\leq b$ and $\sum_{k=1}^{\infty} r^{k-1}=\frac{1}{1-r}$ , then the integral on the left part of equation (a) would be 1. And we have: